In Scenario 1.1 the quaternion measurement is noise-free, i.e., \(q_m=q\) , and the initial angular velocity \(\omega (0)=0.5\bar{u}\) , which favored to stabilize \(\varepsilon _{0}\rightarrow -1\)  as observed in Fig. REF (a). This forced the continuous controller (REF ) to hold the attitude at the beginning, and then to push it to \(\varepsilon _{0} = 1\) . Since \(h\)  is kept a constant for the continuous controller (REF ), no jumps were made to stabilize \(\varepsilon _{0} = -1\) , causing a full rotation known as unwinding phenomenon (Fig. REF (a)). This phenomenon was removed by the hybrid controller (REF ) by performing a jump of the discrete state \(h\)  at 0 \([s]\)  when the gap exceeding \(\delta = 0\) . Notice that this case corresponds to the discontinuous controller of [1]}, and is known not robust to small noise in the measurements. After changing the gap exceeding to \(\delta = 0.4\) , the hybrid controller (REF ) made a jump of the discrete state \(h\)  at \(5\ [s]\)  (Fig. REF (e)), stabilizing \(\varepsilon _{0} = -1\) , (Fig. REF (a)). Note that the exponential convergence of the equilibrium \((e,s)=(0_{4\times 1},0_{4\times 1})\)  is achieved at 30 \([s]\)  for the hybrid controllers, compared with 60 \([s]\)  for the continuous controller (Fig. REF (b) and (c)). Moreover, the continuous controller has a \(23\%\)  more in energy consumption measured by \(\sqrt{\int ^{t}_{0}\tau ^{T}\tau d}\) .
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